Kyoto Journal of Mathematics

Special values of the Hurwitz zeta function via generalized Cauchy variables

Takahiko Fujita and Yuko Yano

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Abstract

As a continuation of the work of Bourgade, Fujita, and Yor, we show how to recover the extension of the Euler formulae concerning some special values of the Hurwitz zeta function from the product of two, and then N, independent generalized Cauchy variables. Meanwhile, we consider the ratio of two independent generalized Cauchy variables and give another proof of the partial fraction expansion of the cotangent function.

Article information

Source
Kyoto J. Math. Volume 52, Number 3 (2012), 465-477.

Dates
First available in Project Euclid: 26 July 2012

Permanent link to this document
https://projecteuclid.org/euclid.kjm/1343309703

Digital Object Identifier
doi:10.1215/21562261-1625163

Mathematical Reviews number (MathSciNet)
MR2959944

Zentralblatt MATH identifier
06081380

Subjects
Primary: 60E05: Distributions: general theory
Secondary: 60G52: Stable processes 11M35: Hurwitz and Lerch zeta functions

Citation

Fujita, Takahiko; Yano, Yuko. Special values of the Hurwitz zeta function via generalized Cauchy variables. Kyoto J. Math. 52 (2012), no. 3, 465--477. doi:10.1215/21562261-1625163. https://projecteuclid.org/euclid.kjm/1343309703


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References

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